Question

A projectile is launched with a speed of $10\text{m/s}$ at an angle ${30}^{\circ }$ with horizontal from a sloping surface of inclination ${60}^{\circ }$. The range $R$ on the incline is
[Take $g=10{\text{m/s}}^2$]

• A. $13.33\text{m}$
• B. $69.28\text{m}$
• C. $32.17\text{m}$
• D. $18.54\text{m}$

Answer 1

The correct option is B $69.28\text{m}$

Take x and y axes in the direction along and perpendicular to the incline as shown below.


Then at point $\text{B}$, displacement $S_y=0$

Using kinematic equation,
$s_y=u_{y}t-\frac{1}{2}{a}_y{t}^2=0$

or $t=\frac{2u_y}{a_y}=\frac{2\times 10}{g\cos {60}^{\circ }}$
$=\frac{2\left(10\right)}{10\times \left(\frac{1}{2}\right)}=4\text{s}$

Now, range on incline, $AB=R=\frac{1}{2}{a}_x\times t^2=\frac{1}{2}g\sin {60}^{\circ }\times t^2$

$=\frac{1}{2}\times (10\times \frac{\sqrt{3}}{2})\times 16$

$=69.28\text{m}$